Using subsurface modifier on circle
You can select the bottom face and use the INSET TOOL (Hotkey : I) to adjust.

But Keep in mind you have a N-GON(poly with more than 4 verts) down there, and subsurf and ngons don't work great together.

You can fix this deleting the NGON face, select all the boundary verts, extrude the verts/edges and scale them to the center